Answer to Question #166833 in Statistics and Probability for Ivy Grace

Question

the time for a major exam to be completed is normally distributed with an average of 55 minutes and a standard deviation of 9 minutes. If 92% of the student completed the exam, when should the test be terminated?

Answer 1

Having a normal distribution with parameters $\mu$ = 55 and $\sigma$ = 9 we need to find the time T: P(t < T) = 0.92 . The same is to find T' = (T - $\mu$) / $\sigma$ , which is the 0.92 quantile of normal distribution with parameters $\mu$ = 0 and $\sigma$ = 1. So T' = 1.41 and T = $\sigma$ *T' + $\mu$ = 9*1.41 + 55 = 67.69.. The test should  be terminated after 67.7 minutes.